Problem: Simplify the following expression: $k = \dfrac{10p - 50}{-20p + 50}$ You can assume $p \neq 0$.
Find the greatest common factor of the numerator and denominator. The numerator can be factored: $10p - 50 = (2\cdot5 \cdot p) - (2\cdot5\cdot5)$ The denominator can be factored: $-20p + 50 = - (2\cdot2\cdot5 \cdot p) + (2\cdot5\cdot5)$ The greatest common factor of all the terms is $10$ Factoring out $10$ gives us: $k = \dfrac{(10)(p - 5)}{(10)(-2p + 5)}$ Dividing both the numerator and denominator by $10$ gives: $k = \dfrac{p - 5}{-2p + 5}$